What are the rotation formulas for a cube?

Question

I have a point (x,y,z)

Suppose I make a 1 by 1 by 1 cube by making eight points at

x -.5, y-.5, z-.5

x +.5, y-.5, z-.5

x -.5, y-.5, z+.5

ect

what would the formulas be for rotating this cube around the axises of the original point x,y,and z in any combination? (its position on the coordinate plane are totally irrelevant for the program i'm using.)

Answer 1

If you are using matrix multiplications, do a search for "matrix transformations 3-d rotation".

If not, then these formulae should suffice:

Rotation about the Z axis:

x' = (x * cos(a)) + (y * -sin(a))

y' = (x * sin(a)) + (y * cos(a))

z' = z

Likewise, a rotation around the Y axis keeps the Y value alone, but involves trig functions on the X and Z values.  Here's the function list for rotating around the Y axis:

x' = (x * cos(a)) + (z * sin(a))

y' = y

z' = (x * -sin(a)) + (z * cos(a))

... and rotation about the x axis uses a similar set of functions.

x' = x

y' = (y * cos(a)) + (z * -sin(a))

z' = (y * sin(a)) + (z * cos(a))